Much of Brazilian Jiu-Jitsu (and grappling) is based on the advancement from one position to a more advantageous position. In grappling tournaments, such as the Abu Dhabi World Submission Wrestling Tournament, points are often awarded simply for improving one's position, without actually inflicting damage on the opponent.
Fundamental positions of Brazilian Jiu-Jitsu:
Rear Mount: The rear mount is the worst possible position for the person on the bottom. It consists of the bottom person being on the ground on their hands and knees (or worse, on their stomach), with the person on top pressing their own stomach against the man on bottom's back, and pinning the opponent's ankles down with their own, a process called "setting the hooks". The best description of this position would be that it looks similar to Anal Sex. The man on bottom is extremely vulnerable to being struck in the back of the head/Medulla area by fists or elbows, as well as being kneed in the ribs. In addition, the man on top can execute the most effective choke in Jiu-Jitsu:the Rear Naked Choke.
Mount: The mount can be described as the top person laying stomach-to-stomach against a person with their back to the ground. It looks very much like sexual intercourse. The top person has a great advantage in leverage, and can attack the bottom person with a variety of strikes, chokes, and armbars. In addition, it can be difficult for the bottom person to breathe, as they have a great deal of weight pinned on their chest.
Side-Mount: Similar to the mount, except the person on top is oriented at a 90 degree angle, as opposed to being directly on top of them. The person on the top puts both of their knees into the side of the person on the bottom, preventing escape. The side-mount is not quite as dominant as the mount in terms of leverage and available techniques. However, it is very effective at taking the wind out of the opponent, giving it the nickname "100 kilos" by Jiu-Jitsu practicioners.
Guard: The guard has numerous variations. When the bottom person has their legs locked together at the ankles around the opponent's back, it is known as the "closed" guard. This is the most advantageous in terms of controlling the other person. An "open" guard is a closed guard where the ankles are not locked. The open guard is less effective at controlling the other person. The concept of passing the guard involves breaking a closed guard into an open one, and then moving into the side-mount. A "half" guard is where the person on the bottom has his legs wrapped around one of the thighs of the person on top. This is an intermediate position often achieved when one is attempting to move from being side-mounted into putting the opponent in the guard. The advantage of the guard in all cases is control: one is able to keep the person on top from acheiving seperation and punching. The two legs wrapped around the opponent's back can also serve in a technique known as the triangle choke, where the opponent is literally choked with their own arm.